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  • Anderson, Dale N. A multivariate Linnik distribution. Statist. Probab. Lett. 14 (1992), no. 4, 333--336. MR1179637
  • Anderson, Dale N.; Arnold, Barry C. Linnik distributions and processes. J. Appl. Probab. 30 (1993), no. 2, 330--340. MR1212665
  • Applebaum, David. Lévy processes and stochastic calculus. Second edition. Cambridge Studies in Advanced Mathematics, 116. Cambridge University Press, Cambridge, 2009. xxx+460 pp. ISBN: 978-0-521-73865-1 MR2512800
  • Balakrishnan, A. V. Fractional powers of closed operators and the semigroups generated by them. Pacific J. Math. 10 1960 419--437. MR0115096
  • Bochner, S. Diffusion equation and stochastic processes. Proc. Nat. Acad. Sci. U. S. A. 35, (1949). 368--370. MR0030151
  • Bogdan, Krzysztof; Byczkowski, Tomasz; Kulczycki, Tadeusz; Ryznar, Michal; Song, Renming; Vondraček, Zoran. Potential analysis of stable processes and its extensions. Edited by Piotr Graczyk and Andrzej Stos. Lecture Notes in Mathematics, 1980. Springer-Verlag, Berlin, 2009. x+187 pp. ISBN: 978-3-642-02140-4 MR2569321
  • Doney, R. A. On Wiener-Hopf factorisation and the distribution of extrema for certain stable processes. Ann. Probab. 15 (1987), no. 4, 1352--1362. MR0905336
  • Erdoğan, M. Burak. Analytic and asymptotic properties of non-symmetric Linnik's probability densities. J. Fourier Anal. Appl. 5 (1999), no. 6, 523--544. MR1752588
  • Grzywny, Tomasz; Ryznar, Michał. Potential theory of one-dimensional geometric stable processes. Colloq. Math. 129 (2012), no. 1, 7--40. MR3007664
  • Jayakumar, K., Suresh, R.P.: Mittag-Leffler distributions. phJ. Indian Soc. Probab. Statist. 7, (2003), 51--71.
  • Kilbas, Anatoly A.; Srivastava, Hari M.; Trujillo, Juan J. Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006. xvi+523 pp. ISBN: 978-0-444-51832-3; 0-444-51832-0 MR2218073
  • Kotz, Samuel; Kozubowski, Tomasz J.; Podgorski, Krzysztof. The Laplace distribution and generalizations. A revisit with applications to communications, economics, engineering, and finance. Birkhäuser Boston, Inc., Boston, MA, 2001. xviii+349 pp. ISBN: 0-8176-4166-1 MR1935481
  • Kozubowski, T. J.; Rachev, S. T. Univariate geometric stable laws. J. Comput. Anal. Appl. 1 (1999), no. 2, 177--217. MR1759045
  • Kozubowski, T. J. Fractional moment estimation of Linnik and Mittag-Leffler parameters. Stable non-Gaussian models in finance and econometrics. Math. Comput. Modelling 34 (2001), no. 9-11, 1023--1035. MR1858835
  • Kozubowski, T. J.; Panorska, A. K. Multivariate geometric stable distributions in financial applications. Math. Comput. Modelling 29 (1999), no. 10-12, 83--92. MR1704767
  • Kozubowski T.J., Rachev S.T.: The theory of geometric stable distributions and its use in modeling financial data, ph% European Journ. Operat. Research., 74, (1994), 310--324.
  • Kuznetsov, Alexey. Wiener-Hopf factorization and distribution of extrema for a family of Lévy processes. Ann. Appl. Probab. 20 (2010), no. 5, 1801--1830. MR2724421
  • Lopez-Mimbela, José Alfredo; Privault, Nicolas. Blow-up and stability of semilinear PDEs with gamma generators. J. Math. Anal. Appl. 307 (2005), no. 1, 181--205. MR2138983
  • Madan D.B., Carr P.P., Chang E.C.: The Variance Gamma Process and option pricing, phEuropean Finance Review, 2, (1998), 79--105.
  • Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni. The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4 (2001), no. 2, 153--192. MR1829592
  • Meerschaert M.M., Benson D.A., Baumer B.: Multidimensional advection and fractional dispersion, phPhys Rev E , 59 (5 A), (1999), 5026--8.
  • Mittnik, Stefan; Rachev, Svetlozar T. Alternative multivariate stable distributions and their applications to financial modeling. Stable processes and related topics (Ithaca, NY, 1990), 107--119, Progr. Probab., 25, Birkhäuser Boston, Boston, MA, 1991. MR1119354
  • Prabhu, N. U. Wiener-Hopf factorization for convolution semigroups. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 23 (1972), 103--113. MR0322970
  • Saichev, Alexander I.; Zaslavsky, George M. Fractional kinetic equations: solutions and applications. Chaos 7 (1997), no. 4, 753--764. MR1604710
  • Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932
  • Sato, Ken-iti. Lévy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4 MR1739520
  • Šikić, Hrvoje; Song, Renming; Vondraček, Zoran. Potential theory of geometric stable processes. Probab. Theory Related Fields 135 (2006), no. 4, 547--575. MR2240700

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